Partial Derivatives-Chain Rule

**DMDil** · April 11th 2009, 08:32 AM

Let

where

??????

??????

Guys, i have this problem from Partial Derivatives chapter-Chain Rule. I don't how to get started in this problem. plz guide me.

**Jhevon** · April 11th 2009, 08:38 AM

Originally Posted by DMDil

Let

where

??????

??????

Guys, i have this problem from Partial Derivatives chapter-Chain Rule. I don't how to get started in this problem. plz guide me.

this is pretty much plugging things into a formula, assuming you knwo how to find partial derivatives.

Note that $W_s = \frac {\partial W}{\partial s} = \frac {\partial F}{\partial s} \underbrace{=}_{\text{chain rule}} \frac {\partial F}{\partial u} \cdot \frac {\partial u}{\partial s} + \frac {\partial F}{\partial v} \cdot \frac {\partial v}{\partial s}$

you want to evaluate these at (1,0)

finding $W_t$ is similar

do you see how to apply the formula in this case? this formula probably wasn't the most efficient way to write it

Note that $W_s(1,0) = \frac {\partial}{\partial s}F(u(1,0),v(1,0))$ , now apply the chain rule, similar to how you did in single variable calc ...(differentiate the outside function, multiply by the derivative of the inside, etc, bearing in mind the first formula i gave. note that i used alternative notation. for example, $\frac {\partial F}{\partial u} \cdot \frac {\partial u}{\partial s}$ means $F_u \cdot u_s$ )

**DMDil** · April 11th 2009, 08:50 AM

Thanks alot, it was like other problem that i done previously, i think it was the format of the problem that confused me, again thanks for showing me.

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